{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Probability distributions in HIC experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We study the relationship between two contigs in a HIC experiments - contig 1 and contig 2, with size $S_1$ and $S_2$, respectively. Our goal is to find out the probability distribution for the number of links between these two contigs, given their distance $D$. We can then compare against the observed number of links to try to infer if the two contigs are linked or not.\n",
    "\n",
    "This distribution is used in the `partition` procedure in [ALLHIC](https://github.com/tanghaibao/allhic). If the two contigs are considered close enough, e.g. $\\Pr(D < threshold) > 0.5$, then we infer the two contigs to be linked. This link graph is then partitioned and distinct partition are then solved independently.\n",
    "\n",
    "We use the following notations:\n",
    "- $S_1$, $S_2$: size of contigs 1 and 2.\n",
    "- $x_1$, $x_2$: start coordinates of contigs 1 and 2. Without loss of generality, we let $x_1 = 0$ and $x_2 > S_1$.\n",
    "- $D$: inner distance between contigs 1 and 2. We require $D > 0$. By definition, we have $x_1 + S_1 + D = x_2$.\n",
    "\n",
    "We build our models based on continuous distributions due to the large size of genomic positions. For each paired reads, we first sample the starting position $x$ uniformly on contig 1, that follows a uniform distribution:\n",
    "\n",
    "$$f(x) = \\begin{cases}\n",
    "            \\frac{1}{S_1}, & 0 \\leq x \\leq S_1 \\\\\n",
    "            0, & \\text{otherwise}\n",
    "         \\end{cases}\n",
    "$$\n",
    "\n",
    "We then consider the length $y$ of this link, that follows a [Pareto distribution](https://en.wikipedia.org/wiki/Pareto_distribution):\n",
    "\n",
    "$$g(y) = \\begin{cases}\n",
    "            \\frac{{\\alpha} y_m^{\\alpha}}{y^{\\alpha + 1}}, & y \\geq y_m \\\\\n",
    "            0, & y < y_m\n",
    "         \\end{cases}\n",
    "$$\n",
    "\n",
    "Where $y_m$ is the smallest observed link length in the dataset. As a side note, we can use the set of intra-contig links to infer the MLE $\\hat{\\alpha}$, using the formula below.\n",
    "\n",
    "$$\\hat{\\alpha} = \\frac{n}{\\sum_{i=1}^{n} \\ln{y_i} - n\\ln{y_m}}\n",
    "$$\n",
    "\n",
    "Now let's come back to the problem of trying to infer the ending position $z$ of the read pair, which is the sum of two random variable $Z = X + Y$. Then $z$ is a convolution of two probability distribution - uniform and Pareto.\n",
    "\n",
    "$$h(z) = \\int_{-\\infty}^{\\infty} f(x) \\cdot g(z - x) dx\n",
    "$$\n",
    "\n",
    "In order to make $f(x)$ nonzero, we need $0 \\leq x \\leq S_1$. In order to make $g(z - x)$ nonzero, we need $z - x \\geq y_m$, borrowing idea from [here](https://math.stackexchange.com/questions/357672/density-of-sum-of-two-uniform-random-variables-0-1), or $x \\leq z - y_m$. Therefore, by comparing $z - y_m$ and $S_1$, we then break this down into two cases:\n",
    "\n",
    "$$h(z) = \\begin{cases}\n",
    "            \\frac{{\\alpha} y_m^{\\alpha}}{S_1} \\int_{0}^{z - y_m} \\frac{1}{(z - x)^{\\alpha + 1}} dx, & y_m \\leq z \\leq S_1 + y_m \\\\\n",
    "            \\frac{{\\alpha} y_m^{\\alpha}}{S_1} \\int_{0}^{S_1} \\frac{1}{(z - x)^{\\alpha + 1}} dx, & z > S_1 + y_m \\\\\n",
    "            0, & \\text{otherwise}\n",
    "         \\end{cases}\n",
    "$$\n",
    "\n",
    "Taking the integral and simplify the formula to closed form:\n",
    "\n",
    "$$h(z) = \\begin{cases}\n",
    "            \\frac{1}{S_1} \\cdot [1 - (\\frac{y_m}{z})^{\\alpha}], & y_m \\leq z \\leq S_1 + y_m \\\\\n",
    "            \\frac{1}{S_1} \\cdot [(\\frac{y_m}{z - S_1})^{\\alpha} - (\\frac{y_m}{z})^{\\alpha}], & z > S_1 + y_m \\\\\n",
    "            0, & \\text{otherwise}\n",
    "         \\end{cases}\n",
    "$$\n",
    "\n",
    "\n",
    "Let's take a look at the shape of this distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1249fa750>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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D6t69e4M/q2+/LWnwcxpLYyxGe/7tPe4pbff+oreuuiyhUWrDjyfrrT36dF/N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\nIkpbDHiIiIiIiChtMeAhIiIiIqK09QvO4N2coq706AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x123a22fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "import math\n",
    "sns.set_context('poster')\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rc\n",
    "#rc('text', usetex=True)\n",
    "#rc('font', **{'family': 'sans-serif', 'sans-serif': ['Helvetica']})\n",
    "\n",
    "ym = 150.\n",
    "S1 = 100000.\n",
    "alpha = .15   # Roughly 1 / [log(100000) - log(150)]\n",
    "\n",
    "def h(z):\n",
    "    if ym <= z <= S1 + ym:\n",
    "        return 1 / S1 * (1 - (ym / z) ** alpha)\n",
    "    if z > S1 + ym:\n",
    "        return 1 / S1 * ((ym / (z - S1)) ** alpha - (ym / z) ** alpha)\n",
    "    \n",
    "x = np.arange(ym + 1, 500000)\n",
    "y = np.array([h(z) for z in x])\n",
    "plt.plot(x, y)\n",
    "ax = plt.gca()\n",
    "ax.set_xlabel(\"Ending position ($z$)\")\n",
    "ax.set_ylabel(\"Probability density\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability distribution for link length distribution\n",
    "\n",
    "For this experiment, we use real data from a draft rice genome and hope to get the best distribution that can quantify the data. Possible candidates are:\n",
    "\n",
    "- Exponential distribution\n",
    "- Bounded reciprocal distribution\n",
    "- Pareto distribution\n",
    "- Bounded Pareto distribution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#fp = open(\"../tests/Chr1/outer.dis.txt\")\n",
    "fp = open(\"outer.dis.txt\")\n",
    "dists = []\n",
    "for row in fp:\n",
    "    contigname, links = row.split()\n",
    "    links = [int(x) for x in links.strip().strip(\",\").split(\",\")]\n",
    "    dists.extend(links)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Critically, the total link distribution is a mixture of regular paired-end sequencing distances (at small distances) and Hi-C link distances (at longer distances). Using a threshold of 1000 separates the two part. But let's take a look first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A total of 411408 small links found (threshold=1000)\n",
      "A total of 7648214 large links found (threshold=1000)\n"
     ]
    },
    {
     "data": {
      "image/png": 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AMEaAAAAAAGCMAAEAAADAGAECAAAAgDECBAAAAABjBAgAAAAAxggQAAAAAIwRIAAAAAAY\nI0AAAAAAMEaAAAAAAGCszwGirKxMHo/Hr82yLBUXF8vr9SohIUErV67U+fPn/WpaWlq0adMmzZ8/\nXx6PR2vWrNGVK1f8ahoaGpSTk6Pk5GQlJSUpNzdXPp/Pr+bSpUt64YUXNGfOHKWmpmrr1q1qaWnp\n62UAAAAAuAvhfSk+efKkXnnllS7tu3bt0p49e7Ru3TrFxsaquLhYmZmZ+uCDDxQVFSVJys/PV3l5\nudavXy+n06mioiKtWrVKhw4d0qhRoyRJq1evVm1trQoKCtTc3KytW7fq6tWrKikpkXQ7hDz11FMa\nO3astm7dqkuXLmnbtm1qbm7Wq6++2t/PBQAAAIA7MAoQLS0t2r9/v3bs2CGn06nW1la7z+fz6Z13\n3lFWVpZWrFghSXrkkUe0YMECHTx4UCtXrtSFCxd0+PBhbd++XYsXL5YkzZw5U+np6SorK9OiRYtU\nWVmpqqoqHThwQAkJCZKkmJgYZWZm6uzZs4qPj9cvfvELXbhwQWVlZYqJiZEkjRkzRgUFBXr++ec1\nceLEgH5yRrIjp+p67PMmxg7gSAAAABBKjG5h+uijj7Rnzx5lZ2crIyPDr+/06dNqampSWlqa3TZu\n3DjNnTtXR48elSRVVlZKkrxer13jdrs1ffp0u6aiokITJkyww4MkJScny+Vy2TXHjh3TQw89ZIcH\nSVq4cKHa2tpUUVHRl+sGAAAAcBeMViBmz56tsrIyRUdHa+fOnX59NTU1kqSpU6f6tU+ZMkXl5eWS\npOrqak2cOFFOp7NLTefx1dXViouL8+t3OByKjY21a2pqauR2u/1q7r33XrlcLrumL8aPd965aIQJ\nD7+dKZ33RPRY09PnrbdjMHDu5v/PQH4tdM4xvv4QLMwxBBtzDMEW6nPMKEBMnjy5xz6fz6eIiAhF\nRPj/cBIZGWlvgG5sbFRkZGSXYyMjI3X58uU71nSex+fz3bEGAAAAQPD0aRN1dyzLUlhYWLd9ne2m\nNQ5H93dU/XV7T+fp6dje3LjR1OdjhrvOpNt0q+cnW/X0eevtGAycu/n/M5BfC51zjK8/BAtzDMHG\nHEOwhcIcmzQpqse+fgeIqKgotbS0qLW1VaNHj7bbGxsb7ScwuVwuNTY2djn28zX19fXd1kybNu2O\n53G5XP29FBjqbYM1AAAAhrd+B4j77rtPlmWptrbW/kFfkt/f3W63rl69qubmZo0dO9avZs6cOXbN\nyZMn/c7d0dGhuro6ff3rX7dramtr/WquX78un8/n97GBkYyABwAAgqnfb6L2eDwaM2aMSktL7baG\nhgYdP35cKSkpkqSUlBS1t7fbm6ql2xuiz50751dTX1+vM2fO2DVVVVXy+Xx2zbx58/TJJ5/Y+yYk\nqbS0VKNHj1ZSUlJ/LwUAAADAHfR7BSIyMlIZGRnasWOHHA6H3G63du/eLZfLpaVLl0qS4uLilJ6e\nrry8PPl8PkVHR6uoqEgzZszQwoULJd0OBwkJCcrKylJ2drba2tq0ZcsWeb1ezZo1S5K0ZMkSFRcX\n65lnntGLL76ozz77TK+//rqWLVumSZMm9fdSAAAAANxBvwOEJK1du1YOh0N79+5VU1OTPB6PNm/e\nbO9vkKTCwkIVFhZq27Zt6ujoUGpqqnJzc+23UIeFham4uFgbN25UXl6eIiIilJaWpg0bNtjnuOee\ne7Rv3z794Ac/0Lp16xQVFaXly5dr7dq1gbgMAJ/DCwUBAMDnhVmWZQ32IAZLff3NwR5CyOnc9X/4\nyLlBHgkGUk9hIBgBIhSeLIHhjTmGYGOOIdhCYY719hSmfu+BAAAAADByECAAAAAAGCNAAAAAADBG\ngAAAAABgjAABAAAAwBgBAgAAAIAxAgQAAAAAYwQIAAAAAMYIEAAAAACMESAAAAAAGCNAAAAAADBG\ngAAAAABgjAABAAAAwBgBAgAAAIAxAgQAAAAAYwQIAAAAAMYIEAAAAACMESAAAAAAGCNAAAAAADBG\ngAAAAABgjAABAAAAwFj4YA8AwOA7cqpusIcAAACGCFYgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAA\nAMAYAQIAAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAA\nAMBY+GAPAMDwcuRUXY993sTYARwJAAAIBlYgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAAAMAYAQIA\nAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAAAMAYAQIA\nAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjIUP9gAQfEdO1fXY502MHcCRAAAAYKhjBQIAAACAsYAF\niPb2dr399tt67LHH5PF4tHTpUlVUVNj9lmWpuLhYXq9XCQkJWrlypc6fP+93jpaWFm3atEnz58+X\nx+PRmjVrdOXKFb+ahoYG5eTkKDk5WUlJScrNzZXP5wvUZQAAAADoRcACxDvvvKM33nhD3/zmN7Vr\n1y7FxcXp2Wef1R/+8AdJ0q5du1RcXKynnnpKRUVFunnzpjIzM3Xz5k37HPn5+fr5z3+ul19+WYWF\nhfr000+1atUqtbe32zWrV6/W8ePHVVBQoA0bNqi8vFwvv/xyoC4DAAAAQC8Ctgfivffe05IlS/Tc\nc89JkpKTk3XixAkdPHhQa9eu1TvvvKOsrCytWLFCkvTII49owYIFOnjwoFauXKkLFy7o8OHD2r59\nuxYvXixJmjlzptLT01VWVqZFixapsrJSVVVVOnDggBISEiRJMTExyszM1NmzZxUfHx+oyxkxPr8/\nwnlPxCCNBAAAAENBwFYgWlpa5HK57L+PGjVKUVFRamho0OnTp9XU1KS0tDS7f9y4cZo7d66OHj0q\nSaqsrJQkeb1eu8btdmv69Ol2TUVFhSZMmGCHB+l2UHG5XHYNAAAAgOAJ2ArE9773Pe3atUuPPfaY\nZs2apUOHDuncuXN66aWXVFNTI0maOnWq3zFTpkxReXm5JKm6uloTJ06U0+nsUtN5fHV1teLi4vz6\nHQ6HYmNj7Zq+GD/eeeeiYaAvqwqOUWF9PgYjU09fP73NnfHjnQoPd/R6PNBfzDEEG3MMwRbqcyxg\nAWL58uWqrKxUZmam3fbSSy8pLS1NJSUlioiIUESE/w8WkZGR9gboxsZGRUZGdjlvZGSkLl++fMca\nNlIDA+v/Vf15QM61KPm+gH0cAADQfwEJEJZl6emnn9b58+eVn5+vBx54QMeOHdOuXbsUHR0ty7IU\nFhbW7bGd7aY1Dkf3d1311N6bGzea+nzMUNR0q8W4tvO3x305BjB140aT/duUv/76622+jZSvUwRO\nd3MMCCTmGIItFObYpElRPfYFJECcOHFCJ06c0JtvvqnHH39c0u29Ce3t7Xr99df1/e9/Xy0tLWpt\nbdXo0aPt4xobGxUVdXtwLpdLjY2NXc79+Zr6+vpua6ZNmxaISwEAAADQi4Bsou68xSgxMdGvfc6c\nObp165bCwsJkWZZqa2v9+mtra+0f/N1ut65evarm5uZeay5evOjX39HRobq6OgIEAAAAMAACEiDc\nbrck6eTJk37tp0+fVnh4uBYtWqQxY8aotLTU7mtoaNDx48eVkpIiSUpJSVF7e7u9qVqSampqdO7c\nOb+a+vp6nTlzxq6pqqqSz+ezawAAAAAET0BuYZo1a5a8Xq9ee+013bhxQw888ICOHz+uf/u3f9OK\nFSsUExOjjIwM7dixQw6HQ263W7t375bL5dLSpUslSXFxcUpPT1deXp58Pp+io6NVVFSkGTNmaOHC\nhZKkefPmKSEhQVlZWcrOzlZbW5u2bNkir9erWbNmBeJSAAAAAPQizLIsKxAnam5u1ptvvqlf/vKX\namho0H333afvfve7+s53vqOwsDC1tbXpzTff1HvvvaempiZ5PB7l5ubqgQcesM/R1NSkwsJC/frX\nv1ZHR4dSU1OVm5uryZMn2zV/+ctftHHjRn344YeKiIhQWlqaNmzY4PcOClP19TfvXDQMfP5lcb1h\nEzWCyZsY2+3GsN7mqDcxNujjwvASCpsPMbwxxxBsoTDHettEHbAAMRQRILoiQCCYCBAYCKHwDy+G\nN+YYgi0U5lhvASJgb6IGAAAAMPwRIAAAAAAYI0AAAAAAMEaAAAAAAGCMAAEAAADAGAECAAAAgDEC\nBAAAAABjBAgAAAAAxggQAAAAAIwRIAAAAAAYI0AAAAAAMEaAAAAAAGCMAAEAAADAGAECAAAAgDEC\nBAAAAABjBAgAAAAAxggQAAAAAIwRIAAAAAAYCx/sAQAYOY6cqpPznghJUtOtlkEeDQAAuBusQAAA\nAAAwRoAAAAAAYIwAAQAAAMAYAQIAAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAAABgjQAAA\nAAAwRoAAAAAAYIwAAQAAAMBY+GAPAADuxpFTdT32eRNjB3AkAACMLKxAAAAAADBGgAAAAABgjAAB\nAAAAwBgBAgAAAIAxAgQAAAAAYwQIAAAAAMYIEAAAAACMESAAAAAAGCNAAAAAADBGgAAAAABgjAAB\nAAAAwFj4YA8AgXPkVN1gDwEAAADDHCsQAAAAAIwRIAAAAAAYI0AAAAAAMEaAAAAAAGCMTdQAQhoP\nBwAAILSwAgEAAADAGAECAAAAgDECBAAAAABjBAgAAAAAxggQAAAAAIwRIAAAAAAYC2iAqKio0NKl\nS/Xwww9rwYIFeuutt9Te3i5JsixLxcXF8nq9SkhI0MqVK3X+/Hm/41taWrRp0ybNnz9fHo9Ha9as\n0ZUrV/xqGhoalJOTo+TkZCUlJSk3N1c+ny+QlwEAAACgBwF7D8SJEyf07LPPasmSJVq7dq3Onj2r\nHTt2yOFwKCsrS7t27dKePXu0bt06xcbGqri4WJmZmfrggw8UFRUlScrPz1d5ebnWr18vp9OpoqIi\nrVq1SocOHdKoUaMkSatXr1Ztba0KCgrU3NysrVu36urVqyopKQnUpYQ0nokPAACAwRSwALF9+3bN\nnz9fmzdvliSlpKToxo0bqqqqUmZmpt555x1lZWVpxYoVkqRHHnlECxYs0MGDB7Vy5UpduHBBhw8f\n1vbt27V48WJJ0syZM5Wenq6ysjItWrRIlZWVqqqq0oEDB5SQkCBJiomJUWZmps6ePav4+PhAXc6A\n6C0MeBNjB3AkAAAAgJmA3MJ07do1nTx5UsuWLfNrX7dund59912dPn1aTU1NSktLs/vGjRunuXPn\n6ujRo5KkyspKSZLX67Vr3G63pk+fbtdUVFRowoQJdniQpOTkZLlcLrsGAAAAQPAEZAXij3/8oyzL\nktPp1HPPPaePP/5YLpdL3/3ud/XCCy+opqZGkjR16lS/46ZMmaLy8nJJUnV1tSZOnCin09mlpvP4\n6upqxcXF+fU7HA7FxsbaNX0xfrzzzkVB5Lwnose+nsbW2zGB4BgVNiAfByPXQMyxnr5+/l/Vn7tt\nX5R8X9DGgoEXHn77d2OD/T0ewxdzDMEW6nMsIAHi+vXrkqTs7GwtWbJEmZmZ+u1vf6vi4mKNGTNG\nlmUpIiJCERH+PzBERkbaG6AbGxsVGRnZ5dyRkZG6fPnyHWvYSA0AAAAEX0ACRGtrqyTp0Ucf1fr1\n6yVJ8+bN0/Xr11VcXKxVq1YpLCys22M72y3LMqpxOLq/66qn9t7cuNHU52MCqelWS499PY2tt2MC\nofO3wsH+OBi5BmKO9fXrZ7C/FyCwOn9jx/9XBAtzDMEWCnNs0qSoHvsCsgeic1XgK1/5il97amqq\nmpqaFB0drZaWFjtodGpsbLSfwORyudTY2Njl3KY1LpcrEJcCAAAAoBcBCRCd+xI+HxDa2tokSeHh\n4bIsS7W1tX79tbW1mjZtmqTbG6avXr2q5ubmXmsuXrzo19/R0aG6ujq7BgAAAEDwBCRAfOlLX9Lk\nyZP1q1/9yq/9ww8/1Be+8AU98cQTGjNmjEpLS+2+hoYGHT9+XCkpKZJuP/a1vb3d3lQtSTU1NTp3\n7pxfTX19vc6cOWPXVFVVyefz2TUAAAAAgicgeyAcDofWrl2r9evXKz8/X+np6Tp27Jjee+89FRQU\nyOVyKSMLEkDLAAAazUlEQVQjw36xnNvt1u7du+VyubR06VJJt1cx0tPTlZeXJ5/Pp+joaBUVFWnG\njBlauHChpNv7KhISEpSVlaXs7Gy1tbVpy5Yt8nq9mjVrViAuBQAAAEAvAvYiuSeffFLh4eEqKSnR\noUOH9MUvflGvvfaavv3tb0uS1q5dK4fDob1796qpqUkej0ebN2+29zdIUmFhoQoLC7Vt2zZ1dHQo\nNTVVubm59luow8LCVFxcrI0bNyovL08RERFKS0vThg0bAnUZAAAAAHoRZlmWNdiDGCz19TcH9ePf\nzZuoezsmEHgKE4JtIOZYX79+ePP78BIKTy/B8MYcQ7CFwhwL+lOYAAAAAIwMBAgAAAAAxggQAAAA\nAIwRIAAAAAAYI0AAAAAAMBawx7gCQKgI9tPKAAAYyViBAAAAAGCMAAEAAADAGAECAAAAgDECBAAA\nAABjBAgAAAAAxggQAAAAAIwRIAAAAAAYI0AAAAAAMEaAAAAAAGCMAAEAAADAGAECAAAAgDECBAAA\nAABjBAgAAAAAxggQAAAAAIwRIAAAAAAYI0AAAAAAMEaAAAAAAGAsfLAHAACh7Mipum7bvYmxAzwS\nAABCAysQAAAAAIwRIAAAAAAYI0AAAAAAMMYeCAAjXk/7HAAAQFesQAAAAAAwRoAAAAAAYIwAAQAA\nAMAYAQIAAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAA\nAMAYAQIAAACAsfDBHgC6d+RU3WAPAQAAAOiCFQgAAAAAxggQAAAAAIwRIAAAAAAYI0AAAAAAMEaA\nAAAAAGCMAAEAAADAGI9xBYAA6+kxzN7E2AEeCQAAgccKBAAAAABjrEAAwF3gZY8AgJGKFQgAAAAA\nxggQAAAAAIwRIAAAAAAYI0AAAAAAMBbwANHS0qLHH39cOTk5dptlWSouLpbX61VCQoJWrlyp8+fP\ndzlu06ZNmj9/vjwej9asWaMrV6741TQ0NCgnJ0fJyclKSkpSbm6ufD5foC8BAAAAQA8CHiD+9V//\nVX/605/82nbt2qXi4mI99dRTKioq0s2bN5WZmambN2/aNfn5+fr5z3+ul19+WYWFhfr000+1atUq\ntbe32zWrV6/W8ePHVVBQoA0bNqi8vFwvv/xyoC8BAAAAQA8C+hjXP/zhD3r33Xd177332m0+n0/v\nvPOOsrKytGLFCknSI488ogULFujgwYNauXKlLly4oMOHD2v79u1avHixJGnmzJlKT09XWVmZFi1a\npMrKSlVVVenAgQNKSEiQJMXExCgzM1Nnz55VfHx8IC8FAAAAQDcCtgLR1tamDRs26Omnn9bkyZPt\n9tOnT6upqUlpaWl227hx4zR37lwdPXpUklRZWSlJ8nq9do3b7db06dPtmoqKCk2YMMEOD5KUnJws\nl8tl1wAAAAAIroCtQLz99ttqbW3VqlWr9F//9V92e01NjSRp6tSpfvVTpkxReXm5JKm6uloTJ06U\n0+nsUtN5fHV1teLi4vz6HQ6HYmNj7Zq+Gj/eeeeiIHLeEzGoH787jlFhkkJzbBgeRvIcG+zvOSNF\nePjt343x+UawMMcQbKE+xwISIM6fP6/du3frxz/+sSIi/H8o8Pl8ioiI6NIeGRlpb4BubGxUZGRk\nl/NGRkbq8uXLd6xhIzUAAAAwMPodIDo6OpSbm6tvfetb8ng8Xfoty1JYWFi3x3a2m9Y4HN3fcdVT\n+53cuNF0V8cFStOtlkH9+N3p/K1wKI4Nw8NInmOD/T1npOj8jR2fbwQLcwzBFgpzbNKkqB77+r0H\n4t1339WlS5f04osvqq2tTW1tbZJu/8Df1tamqKgotbS0qLW11e+4xsZGRUXdHpjL5VJjY2OXc5vW\nuFyu/l4GAAAAAAP9DhClpaW6fPmykpKSFB8fr/j4eH366ac6fPiw4uPjFR4eLsuyVFtb63dcbW2t\npk2bJun2humrV6+qubm515qLFy/69Xd0dKiurs6uAQAAABBc/Q4Qr732mg4ePOj3x+12249pfeKJ\nJzRmzBiVlpbaxzQ0NOj48eNKSUmRJKWkpKi9vd3eVC3d3nx97tw5v5r6+nqdOXPGrqmqqpLP57Nr\nAAAAAARXv/dA3H///V3axo4dq/Hjx2v27NmSpIyMDO3YsUMOh0Nut1u7d++Wy+XS0qVLJUlxcXFK\nT09XXl6efD6foqOjVVRUpBkzZmjhwoWSpHnz5ikhIUFZWVnKzs5WW1ubtmzZIq/Xq1mzZvX3MgAA\nAAAYCOiL5Hqydu1aORwO7d27V01NTfJ4PNq8ebO9v0GSCgsLVVhYqG3btqmjo0OpqanKzc3VqFGj\nJN3eTF1cXKyNGzcqLy9PERERSktL04YNGwbiEgAAAABICrMsyxrsQQyW+vqbg/rxj5yqG9SP352R\n/IQcDIyRPMe8ibE99vX0/aC3Y9C9UHh6CYY35hiCLRTmWG9PYRqQFQgAQGj+0gAAgL7q9yZqAAAA\nACMHAQIAAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAA\nAMAYAQIAAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAA\nAMAYAQIAAACAMQIEAAAAAGPhgz0AAMDdOXKqrtt2b2LsAI8EADCSsAIBAAAAwBgrEAAQwnpaZQAA\nYLCwAgEAAADAGAECAAAAgDECBAAAAABjBAgAAAAAxggQAAAAAIwRIAAAAAAYI0AAAAAAMEaAAAAA\nAGCMAAEAAADAGAECAAAAgLHwwR4AAGDgHDlV1227NzF2gEcCABiqWIEAAAAAYIwAAQAAAMAYAQIA\nAACAMQIEAAAAAGNsogaAYaanjdIAAAQCKxAAAAAAjBEgAAAAABgjQAAAAAAwRoAAAAAAYIwAAQAA\nAMAYAQIAAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAAABgLH+wBAABC25FTdd22exNjB3gk\nAIBQwAoEAAAAAGMECAAAAADGuIUJANDjbUoAAHweKxAAAAAAjAUsQLS3t2vfvn16/PHHlZiYqMWL\nF+unP/2pLMuSJFmWpeLiYnm9XiUkJGjlypU6f/683zlaWlq0adMmzZ8/Xx6PR2vWrNGVK1f8ahoa\nGpSTk6Pk5GQlJSUpNzdXPp8vUJcBAAAAoBcBu4XpRz/6kfbs2aPnn39eiYmJ+t3vfqdNmzbp1q1b\nevbZZ7Vr1y7t2bNH69atU2xsrIqLi5WZmakPPvhAUVFRkqT8/HyVl5dr/fr1cjqdKioq0qpVq3To\n0CGNGjVKkrR69WrV1taqoKBAzc3N2rp1q65evaqSkpJAXQoAAACAHgQkQHSuPjz99NP6x3/8R0lS\nSkqKrl27pr1792r58uV65513lJWVpRUrVkiSHnnkES1YsEAHDx7UypUrdeHCBR0+fFjbt2/X4sWL\nJUkzZ85Uenq6ysrKtGjRIlVWVqqqqkoHDhxQQkKCJCkmJkaZmZk6e/as4uPjA3E5AAAAAHoQkFuY\nfD6fnnzySS1atMivfdq0abp27ZoqKyvV1NSktLQ0u2/cuHGaO3eujh49KkmqrKyUJHm9XrvG7XZr\n+vTpdk1FRYUmTJhghwdJSk5OlsvlsmsAAAAABE9AViDGjRunV199tUv7b37zG8XExNj7GKZOnerX\nP2XKFJWXl0uSqqurNXHiRDmdzi41NTU1dk1cXJxfv8PhUGxsrF3TF+PHO+9cFETOeyIG9eN3xzEq\nTFJojg3DA3Ns+Bjs76E9CQ+//buxUB0fhj7mGIIt1OdY0J7C9LOf/UzHjh3TM888I5/Pp4iICEVE\n+P/AEBkZaW+AbmxsVGRkZJfz9LUGAAAAQPAE5T0Q77//vvLz8/W1r31NGRkZKikpUVhYWLe1ne2W\nZRnVOBzdZ56e2ntz40ZTn48JpKZbLYP68bvT+VvhUBwbhgfm2PAx2N9De9L5G7tQHR+GPuYYgi0U\n5tikSVE99gV8BWLfvn3Kzs6W1+vVtm3bFBYWpqioKLW0tKi1tdWvtrGx0X4Ck8vlUmNjY5fzmda4\nXK5AXwoAAACAzwnoCkRRUZFKSkr05JNP6oc//KHCw2+f/r777pNlWaqtrdW0adPs+r/+u9vt1tWr\nV9Xc3KyxY8f61cyZM8euOXnypN/H7OjoUF1dnb7+9a8H8lIAAHfQ29urvYmxAzgSAMBACtgKxP79\n+1VSUqIVK1Zo8+bNdniQJI/HozFjxqi0tNRua2ho0PHjx5WSkiLp9mNf29vb7U3VklRTU6Nz5875\n1dTX1+vMmTN2TVVVlXw+n10DAAAAIHgCsgLx2Wefadu2bXrwwQf1xBNP6PTp0379s2bNUkZGhnbs\n2CGHwyG3263du3fL5XJp6dKlkqS4uDilp6crLy9PPp9P0dHRKioq0owZM7Rw4UJJ0rx585SQkKCs\nrCxlZ2erra1NW7Zskdfr1axZswJxKQAAAAB6EWZZltXfkxw6dEj/9E//1GN/RUWFoqOj9eabb+q9\n995TU1OTPB6PcnNz9cADD9h1TU1NKiws1K9//Wt1dHQoNTVVubm5mjx5sl3zl7/8RRs3btSHH36o\niIgIpaWlacOGDXe1B6K+/mafjwmk3pb/BwsbXBFszLGRbSBubQqFzYcY3phjCLZQmGO9baIOSIAY\nqggQXfHDHYKNOTayESAwHDDHEGyhMMcG9ClMAAAAAIYvAgQAAAAAYwQIAAAAAMYIEAAAAACMESAA\nAAAAGCNAAAAAADBGgAAAAABgLCBvogYAwERv778ZiHdEAAD6jxUIAAAAAMZYgQAAhDRWLQAgtLAC\nAQAAAMAYKxAAgJDQ20oDACB0sAIBAAAAwBgBAgAAAIAxAgQAAAAAYwQIAAAAAMYIEAAAAACM8RQm\nAMCQ1d2Tm5z3REiSmm61dHsM744AgP5hBQIAAACAMQIEAAAAAGMECAAAAADGCBAAAAAAjBEgAAAA\nABjjKUwAgBGluyc33QlPbgKA/8MKBAAAAABjBAgAAAAAxggQAAAAAIyxBwIAgLvU234K9k0AGK5Y\ngQAAAABgjAABAAAAwBi3MAEAcAd38+hXABiuWIEAAAAAYIwAAQAAAMAYtzABABAEPd32xNOZAAx1\nrEAAAAAAMMYKBAAAA4h3RwAY6liBAAAAAGCMFQgAAEIE+yYADAUECAAAQhy3PQEIJdzCBAAAAMAY\nKxAAAAxh3PYEYKARIAAAGIa47QlAsBAgAAAYYXoLFz0hdADoRIAAAAB3xK1SADoRIAAAwIDi9ipg\naCNAAACAu0YYAEYeAgQAAAgZ7M8AQh8BAgAABMXdhAEAoY8AAQAAhqW7ub2KW7KAOyNAAACAIe1u\nVjr6c4zznghJUtOtlj6fo9PdhJGBCjehHLyG29iGKgIEAADAABuo27tC+TayUP6Be7BDh/OeCC1K\nvi9gHyfQCBAAAABDXCgHkuF2DAgQAAAAgDGCiuQY7AEAAAAAGDqGZIA4cOCAFi1apIcffljf/va3\n9fvf/36whwQAAACMCEMuQLz33nvKz8/XN77xDe3cuVNRUVF6+umndfHixcEeGgAAADDsDakAYVmW\ndu7cqWXLlikrK0t/+7d/q+LiYt17773av3//YA8PAAAAGPaGVID485//rLq6On31q1+120aPHi2v\n16ujR48O4sgAAACAkWFIPYWppqZGknTfff7PxZ06daouXLig9vZ2jRo1yvh848c7Azm8Put8EU0o\ncYwKkxSaY8PwwBxDsDHHEGzMMQSbY1SYwsMdg/6zak+GVIDw+XySpMjISL/2yMhIdXR06NatW3K5\nXMbnGz3aPGwEwxOP3j+oHx8AAACha7B/Vu3JkLqFybIsSVJYWFi3/T21AwAAAAiMIRUgoqKiJEmN\njY1+7Y2NjRo1alSXlQkAAAAAgTWkAkTn3ofPP7L14sWLcrvdgzAiAAAAYGQZUgHC7Xbri1/8okpL\nS+221tZWHTlyRCkpKYM4MgAAAGBkGFKbqMPCwvTss89q48aNGjdunP7mb/5GP/3pT3X9+nVlZmYO\n9vAAAACAYS/M6tyZPITs3btXP/nJT3T9+nV9+ctf1vr16+XxeAZ7WAAAAMCwNyQDBAAAAIDBMaT2\nQAAAAAAYXAQIAAAAAMYIEAAAAACMESAAAAAAGCNAjBDt7e3at2+fHn/8cSUmJmrx4sX66U9/qs49\n9JZlqbi4WF6vVwkJCVq5cqXOnz/vd46WlhZt2rRJ8+fPl8fj0Zo1a3TlypXBuByEsJaWFj3++OPK\nycmx25hfCJSKigotXbpUDz/8sBYsWKC33npL7e3tkphn6L/29na9/fbbeuyxx+TxeLR06VJVVFTY\n/cwx3K2ysrIuTwwN1HxqaGhQTk6OkpOTlZSUpNzcXPl8vuBekIUR4a233rJmzZpl/ehHP7KOHTtm\nvfXWW9aXv/xla8+ePZZlWdbOnTut2bNnW/v377dKS0utb37zm9ajjz5q/c///I99jpycHGvu3LnW\nf/zHf1j/+Z//aT322GPWN77xDautrW2wLgshaPv27daDDz5orV+/3m5jfiEQfve731nx8fHW+vXr\nrWPHjllvv/22NWvWLGvnzp2WZTHP0H8lJSXWl7/8Zau4uNj6+OOPrbVr11rx8fHW2bNnLctijuHu\nnDhxwvJ4PFZiYqJfe6Dm0z/8wz9YCxYssD744APr0KFD1rx586xVq1YF9ZoIECNAW1ub5fF4rDfe\neMOvvaCgwJo3b5518+ZNKzEx0SopKbH7bty4YXk8Hmvv3r2WZVnWn//8Z2vmzJnWL3/5S7umurra\nmjFjhvXrX/96YC4EIe/s2bNWYmKilZycbAcI5hcCZfny5V3+UXz99detjIwM5hkCIj093XrllVfs\nv7e1tVl/+7d/a7322mvMMfTZ//7v/1p79uyx4uPjraSkJL8AEaj5VFFRYT344IPWqVOn7Jpjx45Z\nDz74oPXJJ58E7dq4hWkE8Pl8evLJJ7Vo0SK/9mnTpunatWuqrKxUU1OT0tLS7L5x48Zp7ty5Onr0\nqCSpsrJSkuT1eu0at9ut6dOn2zUY2dra2rRhwwY9/fTTmjx5st1++vRp5hf67dq1azp58qSWLVvm\n175u3Tq9++67zDMEREtLi1wul/33UaNGKSoqSg0NDcwx9NlHH32kPXv2KDs7WxkZGX59gZpPFRUV\nmjBhghISEuya5ORkuVyuoM45AsQIMG7cOL366qt66KGH/Np/85vfKCYmxr6XburUqX79U6ZMUU1N\njSSpurpaEydOlNPp7LEGI9vbb7+t1tZWrVq1yq+9c34wv9Aff/zjH2VZlpxOp5577jnNnj1bKSkp\n2rlzpzo6OphnCIjvfe97+vnPf66KigrdvHlT+/fv17lz57R48WLmGPps9uzZKisr04oVKxQWFubX\nF6j5VF1drbi4OL9+h8Oh2NjYoM658KCdGSHtZz/7mY4dO6Z//ud/ls/nU0REhCIiIvxqIiMj7U04\njY2NioyM7HKeyMhIXb58eUDGjNB1/vx57d69Wz/+8Y+7zCPmFwLh+vXrkqTs7GwtWbJEmZmZ+u1v\nf6vi4mKNGTNGlmUxz9Bvy5cvV2VlpTIzM+22l156SWlpaSopKWGOoU/+ejX+8wL1b2NvNcHcSE2A\nGIHef/995efn62tf+5oyMjJUUlLSJRl36my3LOuONRiZOjo6lJubq29961tdnjAhmc0d5hfupLW1\nVZL06KOPav369ZKkefPm6fr16youLtaqVauYZ+gXy7L09NNP6/z588rPz9cDDzygY8eOadeuXYqO\njuZ7GQIqUPPJsiw5HN3fUNRTeyAQIEaYffv2acuWLfrqV7+qbdu2KSwsTFFRUWppaVFra6tGjx5t\n1zY2NioqKkqS5HK51NjY2OV8f12Dkendd9/VpUuXtGfPHrW1tdntlmWpra2N+YWA6PwN21e+8hW/\n9tTUVP37v/+7oqOjmWfolxMnTujEiRN688039fjjj0u6fS95e3u7Xn/9dX3/+99njiFgAvVvo8vl\nUn19fbc106ZNC9Lo2QMxohQVFWnz5s36u7/7O7311lv2stl9990ny7JUW1vrV19bW2tPPrfbratX\nr6q5ubnHGoxMpaWlunz5spKSkhQfH6/4+Hh9+umnOnz4sOLj4xUeHs78Qr913uPbuRLRqTO0Ms/Q\nX523hCQmJvq1z5kzR7du3VJYWBhzDAETqJ+93G63Ll686Nff0dGhuro6AgT6b//+/SopKdGKFSu0\nefNmhYf/3+KTx+PRmDFjVFpaarc1NDTo+PHjSklJkSSlpKSovb1d5eXldk1NTY3OnTtn12Bkeu21\n13Tw4EG/P263WwsWLNDBgwf1xBNPML/Qb1/60pc0efJk/epXv/Jr//DDD/WFL3yBeYZ+c7vdkqST\nJ0/6tZ8+fVrh4eFatGgRcwwBE6ifvVJSUlRfX68zZ87YNVVVVfL5fEGdc9zCNAJ89tln2rZtmx58\n8EE98cQTOn36tF//rFmzlJGRoR07dsjhcMjtdmv37t1yuVxaunSppNu//UtPT1deXp58Pp+io6NV\nVFSkGTNmaOHChYNxWQgR999/f5e2sWPHavz48Zo9e7YkMb/Qbw6HQ2vXrtX69euVn5+v9PT0/9/e\n3aooEAVQHD9TLIpZk2GSMCA2MQ34AEbFYLGaBZ2iGNQ2YBLER3CKBqNFweIr+AKClsEgzoYFYcMu\nl3WEhf3/4p3LZcIpB+6HdrudgiBQv99XKpUiZ3iJ4zhyXVeDwUCXy0W2betwOGg+n6vZbCqTyZAx\nxCaZTMaSp1KppEKhoHa7rU6no/v9rslkItd15TjO2/7fiqIoetvq+BOWy6W63e633/f7vdLptHzf\nVxAECsNQxWJRnufJtu3nvDAMNRqNtNls9Hg8VC6X5Xnej7cM4H+qVqvK5/Maj8eSPreZkC/EYbVa\naTab6XQ6KZvNqtVqqVarSSJneN3tdpPv+1qv17per8rlcmo0GqrX67Isi4zh16bTqRaLhY7H43Ms\nrjydz2cNh0Ntt1slEglVKhX1er0vb5rEjQIBAAAAwBhnIAAAAAAYo0AAAAAAMEaBAAAAAGCMAgEA\nAADAGAUCAAAAgDEKBAAAAABjFAgAAAAAxigQAAAAAIx9AAK3gvBlb1khAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11276aa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "threshold = 1000\n",
    "dists = np.array(dists)\n",
    "\n",
    "dists_small = dists[dists < threshold]\n",
    "sns.distplot(dists_small, bins=100, kde=False)\n",
    "print(\"A total of {} small links found (threshold={})\".format(len(dists_small), threshold))\n",
    "\n",
    "dists_large = dists[dists > threshold]\n",
    "print(\"A total of {} large links found (threshold={})\".format(len(dists_large), threshold))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x118411cd0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SJOror/tbVV5Rcsr98Bi/bDt20Wfy+Q7zcR4hWziXkC2cS/mTUWCvq6vLdR15\n1zfCPrKA/dwrB9J+rq8t0/tHOtXeGdDmX76lMyaVpT1/9cenj65QAAAAFJQxbUhvb+8ey7cbkcSN\nk1yWpe6eU1/hZVpdLLBL0u4DrZpQnj5ab/LvANmRGHngnzVGg/MI2cK5hGzhXMq92tryQbezDrsk\nx3GSyzqOtoWlYVJZ8hgHDncqEo0O8woAAABgaAR2SeFI302O7FNc0jHBY7vUEG+DCYWjambyKQAA\nAEaBwK7R3+W0v5lTK5KP3zvUOerjAQAAoHAR2NW3Qox06jdNSjW1xidvfCb1waP+tOMDAAAAI0Fg\nV99Nk6TR97DHjuHStMmxSQORqJOchAoAAACM1IgD+6233qrXX389F7XkTbYDuyTNmkJbDAAAAEaP\nEXZJ4bSWmOz8SiZNKFFJkVuSdOh4l3oC4awcFwAAAIWFwK6+Ndil7I2wuyxLMybHRtkdJ7bEIwAA\nADBSBHb1m3SapcAusVoMAAAARo/ArvQedjtLLTGSNLGiSOU+jySppb1H/u5Q1o4NAACAwkBgV78e\n9iyOsFuWpZmpk08Pd2Tt2AAAACgMBHb162HPwjrsqWZOKU8+fvfgCUWirMkOAACAzBHYlbsedkmq\nLCvSpOoSSVJnd0ivvHUkq8cHAADA6Y3Arv7rsGf/V3L+7InJx//9xwOKRp2svwcAAABOTwR29V+H\nPbsj7JI0ZaJPNZXFkqQjrd165W+MsgMAACAzBHbl5k6nqSzL0kfPrEn+/N8v7WeUHQAAABkhsCu9\nhz2byzqmmlrTN8p+uLVbr+5mlB0AAADDI7ArN3c67c+yLJ1/ZkovO6PsAAAAyACBXf1WiclBD3tC\nfU2pZkyOLfN46Hi3XttzNGfvBQAAgNMDgV39l3XM3a/Esixdd8nM5M///dJ+RR1G2QEAADA0Arty\nP+k01UdnT9T0+Ch787Eu/WlPS07fDwAAAOMbgV25X9YxlWVZuu7iGcmftz7/rk74Azl9TwAAAIxf\nBHb1n3Sa+1/JvDNrkr3sx070avUv3pC/J5Tz9wUAAMD4Q2BX/x723I6wS7FR9q9cf56qy4skSc0t\nXfrJ1jfVEwjn/L0BAAAwvhDY1a+HPcctMQm1VSX65o3zVFbikSTt+7BD9z35F4VSRvsBAAAAArv6\nethdliWXNTaBXZKm1pTqmzfOU0mRW5L0twNtuv/pXQpHosO8EgAAAIXCzncBJkj0sNtjMLr+whvN\nA7Zd9tHy5NV1AAAcBUlEQVSp2vbaQUWijt5495h+9LOdurhxsqz4xcPCefU5rwsAAABmYoRdfT3s\nbnd+fh11E3xaOL9eifb5fR92sNwjAAAAJBHYJaUG9rFrh+mvvrZUl3x0avLnt/a3add7rXmrBwAA\nAGYgsKsvsNtjsKTjycyYXK4Fcyclf/7Tnhbt+/BEHisCAABAvhV8YHccJ7lKTD5H2BPOnl6txlkT\nkj+/9JfD+uu+43msCAAAAPlU8IE9dUUWO0897P3NO6tGZ9ZXSpIcR1r31F/13qGOPFcFAACAfDAj\noebRWN80KROWZekT59bpjNpSSVIgFNH/+b+v65c79rNOOwAAQIEp+MCeetMkU0bYJcnlsnTZvKmq\nrSqWJAWCET3xu336zkOv6H92H5XjOHmuEAAAAGPBnISaJ6E83OU0U7bbpasuOEOXnD9FicqOnejV\n/U//VT/62U7tP0ybDAAAwOmu4AO7qSPsCV6PW1/8zFzdfsuFmtNQldz+zsET+v7m1/TsH95TNMpo\nOwAAwOnKvIQ6xsIG9rAPZvrkcq24ab6W/cN5yTYZx5Ge/sN7+j//uVPHT/TmuUIAAADkgp3vAvIt\nmDKJ08QRdkl64Y3mtJ+vXtCgP797XH/ZF7ux0tsHT+g7D72si86brOmTyyVJC+fVj3mdAAAAyD4z\nE+oYMnGVmOG4XS7N/0itrr6wQb6i2DVXMBzV7974UC/95ZA6u4N5rhAAAADZUvCB3fQe9pOZPNGn\nay+eoYZJZclte5s79NSL72ntE3/W3/a3spoMAADAOFfwLTFhg1eJyUSx162F86fq7Q/a9druFkXi\nE1Bff+eYXn/nmOprS/X3f9egixsny+0aXxckAAAAYIQ9rYfdPc5G2BMsy9KcadVafPksnT97ooq9\n7uRzzS1d2vT/7db/3vg/2vN+Wx6rBAAAwKko+BH29JaY8TfCnqqkyNa8s2rUOHuCSry2fvPaQR04\n3CkpFtxX/efrWjB3kv7xijM1oaI4z9UCAAAgEwUf2NMnnY7PEfb+3C6XPnneFF107mTteb9d/7nt\nHR1s8UuSXv3bUb357nFd+8npunxevcpKPHmuFgAAACdDYD+NRthTpS4Fmehxf+OdYwqGowqEInri\nd/v01Iv7VF9bpplTynXGpDJ96oKGPFYMAACAwRDYT8MR9v5cLktnT6/WjCnl2vn2Mb178IQkKepI\nHxz164OjftluS+992Kkr5tdrdn2FLOv0uXgBAAAYzwo+sKffOOn0DqnFXlufPG+y5kyr0rsHT+jA\n4U71BmOfPxxxtGPXYe3YdVgzJpfr7y9s0IVnTxp3S10CAACcbgo+sKeNsBdIOJ1YUayJ5xTrwrMn\n6dDxbr13qEPvH+lUOBJbEnL/4U499N9v6fHn39UV8+t10bmTVVtVkueqAQAAChOB/TTtYc+Ey2Wp\nvrZU9bWlCkfq5LXd+s3/fKDmY12SpBP+oJ7+/Xt6+vfvqb62VPPOrNG8s2o0c0qFXLTMAAAAjAkC\newH0sGfCdrsUdRxdeUG9Dh3v1u4DbTrY0pV8vrmlS80tXfrljgMq9ro1Y3K5/p+rztK0uvI8Vg0A\nAHD6K/jAfjqtw54NlmVpak2pptaUqqMrqH0fduhgi1+tHYHkPr3BiHa/367/vfF/NG1SmS4+P7aE\nJEtEAgAAZF/BB/bwgB52J3/FGKai1Kt5Z8XaYLp6Qzp4tEsHj/p16HiXovFf0/tH/Xp/2zva+vy7\nmjW1UtMmlamhrkzTJpVrak2pPHbhfmsBAACQDQUf2NNWiXFZikYJ7IMpLfZozrQqzZlWpd5gRO8d\n6tCR4916/2jshkzhiKO3P2jX2x+0J1/jdlmaOaVCHz1zoj46u0b1taUsFwkAADBCBR/Y+68SE41G\nT7I3JKnY69bc6dWaO71axzt6tffgCR040qmeQCRtv0jU0bvNJ/Ru8wk98bt9Ki22tWBuneZOr1Z9\nbakmVZcU9LwBAACATBR8YO/fwx4K5bGYcSixROSCc+rUEwirtSOg1s5etXUEdOxEr/w9fb/Qrt6w\nnn+9Wc+/HrsLq+12aepEn+prSzW9rlxzZ0xQfW0pK9AAAACkKPjAnhhht90u2jVGqaTIVn2trfra\n0uS2jq6gDh7162BLl460dctJ6TgKR6KxHvijfu3YdUSSVO7zaO70ap0zY4LmNFSptqpELhf/XAAA\nQOEisMd72L1MjsyJilKvzpk5QefMnKBgKKJDx7vV2tGrNn9Q7Z2BtBF4SersDunVvx3Vq387KinW\nB19fU6opNaWaOtGnM2rLdOYZlSr3efPxcQAAAMZcwQf2REuM1+POcyWnP6/HremTyzV9ct/a7aFw\nVO3+gI629ejQ8W4dbetO3nFVivXBJ0bhU51RW6azp1VpzrRqfaSBAA8AAE5fBR/YE8s6svxgfnhs\nl2qrSlRbVaJzZ05QJOroWHtPciS+3R9UV09owGKbB1v8Otji17Y/HZQkTago0hm1ZaqvLdUZtWU6\no7ZMUyb6ZLv55woAAMa3gg/sjLCbxe2yVDfBp7oJvuS2cCSqjq6g2v1BHTvRoyOtPWrrDKS9rrUj\noNaOgP6893jasSbH22jOqC1VfW2Z6qpLVFNZwgUaAAAYNwo6sDuOk5x0Sg+7uWy3SxMqijWholiz\nplZIknqDYR1p7dGR1m61nOjVCX8grZVGirXTNLd0qbmlS6+kbLckVVcUqbYyNrI/taZU0+rKNK2u\nnLu1AgAA4xR0YA9H+pZ0ZIR9fCn22mn98I7jqLM7pHZ/QG2dAbV3BtTmD6qzKzigncZR34j8npQb\nPUmx1pppk8pVN6FEE8qLVV1eFL9YKFJFqZclJwEAwJgr6MCeetMkWiTGN8uyVFHqVUWpV9Pq+ia1\nhiNRnfAH1e4PqN0fUGd3SJ3dIfm7QwpFBt4kKxHkB+N2WaouL+oL8f3/rihihB4AAGRdQQf21Jsm\nMcJ+erLdLk2sLNbEyuK07Y7jKBCKqrM7qLbOgFo7etXaEQv1/VtrEiJRR8dO9OrYiV5JJwbdx2u7\nVFsduxlUTUWxpkz0acrEUtVNKJGvyGatfwAAMGIFHdhTR9jpYS8slmWp2OtWsTfWx54QdRz5u0Py\n94TU1RtWd2/s766ekLp7w+rqDQ0Z6KXYRWBzi1/NLf4Bz3lslypLvaos86qytEiVZd7YnWIrYhcU\nEyuKVVlG2w0AAEhX0IGdEXb050pprRlKMBRJD/P9An1XT0jRQTJ9KBxNGaEfnNtlxQN9X6ivLI0F\n+5qqEtVUxvrqWa4SAIDCUdCBPUwPO06B1+OW1+NWdXnRoM8XFXnU2RXU4eN+dXQFdaIrKH93SD2B\nsHoCkUF75xMiUSelj75z0H0sS6ouL1KJ15bbbcntcsl2W7LdLpX7PKqpLFFNVXFsffvKYpX7vPJ6\nXHK7OMcBABiPCjqwB8OR5GNG2JEtbpelqvIiee3BW1tC4ah6g+HkiLy/JzZC3xUfse8JhBUMDR3q\nHUfxQD/45Nih2G5LXtstj8clX5Gt6vIiVZUVJf+uKPWqyONSUfyCpMjjVkmRrXKfhxF9AADyqMAD\ne2pLDIEEY8Nju+SxvSr3Dd1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03HPP6ZlnntFdd90ll6ugv2DHCAw2Sbm4uFhVVVVqbGzM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\nDPb/AzhQcc4WCSArAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11192f610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(dists_large)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   5666   30471    4471 ..., 1528691 7903357  810442]\n",
      "[  8.64223868  10.32453069   8.40536738 ...,  14.23992237  15.88279816\n",
      "  13.60533506]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1183fb750>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x123ae5a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's look at log-log plot\n",
    "logdists = np.log(dists_large)\n",
    "print(dists_large)\n",
    "print(logdists)\n",
    "sns.distplot(logdists, kde=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.260956856607 -9.57593963391 0.820223231535 8.20113443983e-117 0.00836826042947\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1214b2b10>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vX8Kon+XIUGHmORgkYcRluL/6svRwfAJZq9ar2/AXdHrSMVLREB4qzBuTHBfN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121510d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y, x = np.histogram(logdists, bins=500)\n",
    "y = np.array(y, dtype=\"float\") / y.sum()\n",
    "plt.semilogy(x[:len(y)], y, 'r-', basey=10)\n",
    "\n",
    "from scipy import stats\n",
    "N = 500 * 19 / 20\n",
    "px = x[:N]\n",
    "py = np.log(y)[:N]\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(px, py)\n",
    "print slope, intercept, r_value, p_value, std_err\n",
    "plt.semilogy(px, np.exp(slope * px + intercept), 'g:', basey=10)\n",
    "\n",
    "# y = exp(slope * log(x) + intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.1142688   0.06771425  0.04599064  0.03459755  0.02782625  0.02308199\n",
      "  0.01972805  0.01722868  0.0153176   0.01374501]\n",
      "[   1001.      20998.984   40996.968   60994.952   80992.936  100990.92\n",
      "  120988.904  140986.888  160984.872  180982.856]\n",
      "-2.70947725941e-07 -5.59522201219 -0.871778958948 1.10703950997e-148 7.00092599758e-09\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x130abc8d0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WS6Zpc0UAAACobwgJkcYw5OveQ5LkKC6ScwuLlwEAABBehIQI5O3OlCMAAADYh5AQgXzd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\niIiISID/B2Oc+/3El+idAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112783890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dd = dists_large[(dists_large > 1000) & (dists_large < 10000000)]\n",
    "y, x = np.histogram(dd, bins=500)\n",
    "y = np.array(y, dtype=\"float\") / y.sum()\n",
    "print(y[:10])\n",
    "print(x[:10])\n",
    "#plt.plot(x[:len(y)], y, 'r-')\n",
    "plt.semilogy(x[:len(y)], y, 'r-', basey=10)\n",
    "#plt.loglog(x[:len(y)], y, 'r-', basex=2)\n",
    "\n",
    "# The regression of log(y) ~ x\n",
    "from scipy import stats\n",
    "N = 500 * 19 / 20\n",
    "px = x[:N]\n",
    "py = np.log(y)[:N]\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(px, py)\n",
    "print slope, intercept, r_value, p_value, std_err\n",
    "plt.semilogy(px, np.exp(slope * px + intercept), 'g:', basey=10)\n",
    "\n",
    "# y = exp(slope * x + intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7648214, 3982571.6774392035)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(dists_large), dists_large.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DescribeResult(nobs=8059643, minmax=(150, 43257092), mean=3779286.7311464045, variance=39198176905001.609, skewness=2.348629306588913, kurtosis=5.7953127923320675)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 100000)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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U4HE4HJo/f75mzJghX19f40nLkuR0OpWUlKQuXbpoxIgRkqSoqCjt379fX3/9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\nBB4AAAAAlkXgAQAAAGBZBB4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jR4+Wz+dTZWWlVZORkaGOHTv61Zw+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\nCDwBaHn/YE1Njd94TU2NkpKSWuGI8H1ZvHixiouL9dBDD2nJkiXWZd7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1214e8350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "print(stats.describe(dists))\n",
    "logdists = np.log(dists)\n",
    "ax = sns.distplot(dists, bins=1000, kde=False)\n",
    "\n",
    "# Reciprocal\n",
    "\n",
    "ymm = dists.min()\n",
    "yma = dists.max()\n",
    "\n",
    "def reciprocal_pdf(t, ymm, yma):\n",
    "    \"\"\" Reciproal pdf, there is no param other than the two bounds\n",
    "    \"\"\"\n",
    "    return 1 / ((math.log(yma) - math.log(ymm)) * t)\n",
    "\n",
    "t = np.arange(ymm, 100000)\n",
    "line, = plt.plot(t, reciprocal_pdf(t, ymm, yma) * (100000 - ymm), \"b-\")\n",
    "line.set_label('Reciprocal(bounds=({}, {}))'.format(ymm, yma))\n",
    "ax.legend()\n",
    "ax.set_xlim(0, 100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x124539750>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HEKhnhmF4pgeV28t18rsSkysCAABAY0QQMAH3EwAAAIDZCAIm8Fow/DkLhgEA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\nRERR6P8DxTOD7gBhjzsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122879b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exponential\n",
    "lambda_hat = 1 / np.mean(dd)\n",
    "ymm = dd.min()\n",
    "\n",
    "def exponential_pdf(t, L):\n",
    "    \"\"\" Returns pdf for exponential distribution\n",
    "    \"\"\"\n",
    "    return L * np.exp(-L * t);\n",
    "\n",
    "t = np.arange(0, 40000000, 20)\n",
    "#line, = plt.semilogy(t, exponential_pdf(t, lambda_hat), \"m-\", basey=10)\n",
    "line, = plt.plot(t, exponential_pdf(t, lambda_hat), \"m-\")\n",
    "line.set_label('Exp({:.6g})'.format(lambda_hat))\n",
    "plt.gca().legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112d3af10>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PB/3073++zj67l5Yvf169ep0jh8Oh/Pw8vfvuHwPP27dvrz7++CMNGjQk8Dpz5jyuv/3t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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efe8790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Pareto\n",
    "import math\n",
    "\n",
    "ymm = dists.min()\n",
    "alpha_hat = len(dists) / (np.log(dists).sum() - len(dists) * math.log(ymm))\n",
    "\n",
    "def pareto_pdf(t, alpha, ymm):\n",
    "    \"\"\" Returns pdf for Pareto distribution\n",
    "    \"\"\"\n",
    "    return alpha * ymm ** alpha / t ** (alpha + 1)\n",
    "\n",
    "t = np.arange(ymm, 100000)\n",
    "line, = plt.plot(t, pareto_pdf(t, alpha_hat, ymm) * (100000 - ymm), \"g-\")\n",
    "line.set_label('Pareto({:.6f}, {})'.format(alpha_hat, ymm))\n",
    "plt.gca().legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112d61590>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SpUpKTz9YbLv09IPe29s5HA4VFBT4PZ+dnVOm4xbu69ChQ37rC4OvVBQwR44co2bNmhfb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\n7IQQQgghhPAYDdgJIYQQQgjhsb8AQSv/3JZbFJsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f5a8b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bounded Pareto\n",
    "import math\n",
    "\n",
    "ymm = dists.min()\n",
    "yma = dists.max()\n",
    "alpha_hat = .01\n",
    "\n",
    "def bounded_pareto_pdf(t, alpha, ymm, yma):\n",
    "    \"\"\" Returns pdf for Pareto distribution\n",
    "    \"\"\"\n",
    "    return (alpha * ymm ** alpha / t ** (alpha + 1)) / (1 - (ymm / yma) ** alpha)\n",
    "\n",
    "t = np.arange(ymm, 100000)\n",
    "line, = plt.plot(t, bounded_pareto_pdf(t, alpha_hat, ymm, yma) * (100000 - ymm), \"k-\")\n",
    "line.set_label('BoundedPareto({:.6f}, {})'.format(alpha_hat, ymm))\n",
    "plt.gca().legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1130a9790>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1m5kzZ2rGjBmaN2+esrKy1LhxY02YMEHXX3+9JGns2LGy2+1avHix8vLy1K5d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\nnBybeiIiIiIiJ8emnoiIiIjIyf0PGxu9JxCTHNwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115abe1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Reciprocal\n",
    "\n",
    "ymm = dists.min()\n",
    "yma = dists.max()\n",
    "\n",
    "def reciprocal_pdf(t, ymm, yma):\n",
    "    \"\"\" Reciproal pdf, there is no param other than the two bounds\n",
    "    \"\"\"\n",
    "    #return (math.log(yma) - math.log(ymm)) / t\n",
    "    return 1 / ((math.log(yma) - math.log(ymm)) * t)\n",
    "\n",
    "t = np.arange(ymm, 100000)\n",
    "line, = plt.plot(t, reciprocal_pdf(t, ymm, yma) * (100000 - ymm), \"b-\")\n",
    "line.set_label('Reciprocal(bounds=({}, {}))'.format(ymm, yma))\n",
    "plt.gca().legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma (0.41089698509217443, 149.99999999999997, 55108.379832583487)\n"
     ]
    },
    {
     "data": {
      "image/png": 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FxcX+fbW1tdqzZ4/S09MlSenp6WpsbPQ/EEC6fDP+Bx98EDBz5swZvf/++/6Z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\nlZXjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1162af150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import scipy.stats\n",
    "\n",
    "a, b = ymm, 100000\n",
    "size = b - a\n",
    "x = scipy.arange(a, b)\n",
    "y = dists\n",
    "h = plt.hist(y, color='w', bins=500)\n",
    "\n",
    "#dist_names = ['gamma', 'beta', 'rayleigh', 'norm', 'pareto']\n",
    "dist_names = ['gamma']\n",
    "\n",
    "for dist_name in dist_names:\n",
    "    dist = getattr(scipy.stats, dist_name)\n",
    "    param = dist.fit(y)\n",
    "    print dist_name, param\n",
    "    pdf_fitted = dist.pdf(x, *param[:-2], loc=param[-2], scale=param[-1])\n",
    "    plt.plot(pdf_fitted, label=dist_name)\n",
    "    plt.xlim(0, b)\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability of an inter-contig link fall within contig 2\n",
    "\n",
    "From the $h(z)$ distribution, we are mostly interested in the second case, when the ending position occurs after contig i.e. $z > S_1$, beyond the extent of contig 1, so that it becomes a inter-contig link, rather than intra-contig link. The integral when $z > S_1$ is the following:\n",
    "\n",
    "$$\\Pr(z > S_1) = 1 - \\Pr(z \\leq S_1) = 1 - \\frac{1}{S_1} \\int_{y_m}^{S_1} 1 - (\\frac{y}{z})^{\\alpha} dz \n",
    "                = \\frac{S_1 (\\frac{y_m}{S_1})^{\\alpha} - \\alpha y_m}{S_1 (1 - \\alpha)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44333858891237005"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(S1 * (ym / S1) ** alpha - alpha * ym) / (S1 * (1 - alpha))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is just a normalizing constant $C$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 10000)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JCmym93q9+vd//3d95zvfabd/0ZAcNqPS6mntkc8AAAAALlQdLjYL7hH58lHENTU1ysnJ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\nIiIiIoo6DCpERERERBR1/j8jIVwI/Hw5XAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112d9af10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "C = (math.log(1000000) - math.log(ym))\n",
    "\n",
    "def reciprocal(z):\n",
    "    return 1 / (z * C)\n",
    "\n",
    "def pareto(z):\n",
    "    return alpha * ym ** alpha / z ** (alpha + 1)\n",
    "\n",
    "\n",
    "y1 = np.array([reciprocal(z) for z in x])\n",
    "y2 = np.array([pareto(z) for z in x])\n",
    "plt.plot(x, y1, 'r-')\n",
    "plt.plot(x, y2, 'g-')\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(0, 10000)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
